2024/04/25 by Nicolas Camps, Gigliola Staffilani, Camps, Nicolas +1
Mathematics · #35B40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40
paper · pdf · doi:10.48550/arxiv.2404.16817
Minor changes
arxiv created 2026/07/31 · arxiv updated 2026/08/04
We consider the cubic Schrödinger equation posed on a product space subject to a generic Diophantine condition. Our analysis shows that the small-amplitude solutions undergo modified scattering to an effective dynamics governed by interactions that induce no growth of high-order Sobolev norms. This is in sharp contrast with the infinite energy cascade scenario observed by Hani--Pausader--Tzvetkov--Visciglia in the absence of Diophantine conditions.